System-environment correlations for dephasing two-qubit states coupled to thermal baths

TL;DR

This paper analyzes the dynamics of system-environment correlations in a two-qubit system undergoing dephasing due to a thermal bath, revealing temperature-dependent entanglement behaviors and complex correlation oscillations.

Contribution

It provides exact criteria for separability and entanglement between a two-qubit system and its environment, highlighting temperature effects and correlation oscillations during decoherence.

Findings

Entanglement between system and environment forms below a critical temperature.

Total state remains separable during initial decoherence.

SE correlations oscillate between separable and entangled states near T_crit.

Abstract

Based on the exact dynamics of a two-qubit system and environment, we investigate system-environment (SE) quantum and classical correlations. The coupling is chosen to represent a dephasing channel for one of the qubits and the environment is a proper thermal bath. First we discuss the general issue of dilation for qubit phase damping. Based on the usual thermal bath of harmonic oscillators, we derive criteria of separability and entanglement between an initial $X$ state and the environment. Applying these criteria to initial Werner states, we find that entanglement between the system and environment is built up in time for temperatures below a certain critical temperature $T_{\mathrm{crit}}$. On the other hand, the total state remains separable during those short times that are relevant for decoherence and loss of entanglement in the two-qubit state. Close to $T_{\mathrm{crit}}$ the SE correlations oscillate between separable and entangled. Even though these oscillations are also observed in the entanglement between the two qubits, no simple relation between the loss of entanglement in the two-qubit system and the build-up of entanglement between the system and environment is found.